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Factors of 98

Factors of 98

 

Prime factors are those numbers that, when divided by 98, do not leave any remainder. This implies that the number 98 must be completely divisible by the number, which will be its factor.

  • Only integers and whole numbers can be factored in and will have factors.
  • Only the composite numbers can be factored in because they are made from the product of two or more numbers.
  • Every factor of a number is equal to less than the number itself.
  • The factors of a number are finite. It means, universally, that number will have specific factors only.

The number 98 can be divided into factors of different smaller numbers. There are six factors of 98, out of which 98 is the largest.

The factors of 98 are: 1, 2, 7, 14, 49 and 98. These factors are positive integers. The pair of factors of 98 are: (1, 98), (2, 49), and (7, 14).

The prime factors of 98 are: 1, 2 and 7. 14 and 49 are not prime factors as they are also factorable numbers.

Negative factors of 98 are: -1, -2, -7, -14, -49 and -98. Prime factorization of 98 is 2 x 7 x 7 = 2 x 7²

How to find the factors of 98?

The factors of 98 can be found by two methods – Prime factorization method and Long-division method.

Factors of 98 Prime factorization method

The prime factorization method is the most common method to represent 98 or any other number. Its other form, the prime factor tree method, is a visual method to represent factors of 98. It helps in determining various prime factors of 98. A factor tree is not unique for a given number. Instead of expressing 98 as 2 x 49, we can express 98 as 2 x 7 x 7.

We need to divide 98 from the smallest number to the biggest number as shown-

image
  • With the help of divisibility rules, we need to find out the smallest factor of the given number. Here, we have 98, which is an even number. It is divisible by 2. In other words, 2 divides 98 with no remainder. Therefore, 2 is the smallest prime factor of 98.
  • 98 ÷ 2 = 49. We need to repeat the steps with other numbers until we get the remainder of 0.
  • 49 is not further divisible by 2. So we need to find another number that divides 49 completely.
  • 49 ÷ 7 = 7. Here, 7 is the quotient. Now, we need to divide it by other numbers and find the prime factors of the 7.
  • 7 ÷ 7 = 1. Here, we get remainder 1. After this, our process is completed, and we get factors of 98.

Prime factorization of 98 using the prime factorization method is 2 x 7 x 7 = 2 x 72.

Example 1: What are the common factors of 98 and 49?

Solution:

The factors of 98 are 1, 2, 7, 14, 49 and 98.

The factors of 49 are 1, 7 and 49.

Thus, the common factors of 98 and 49 are 1, 7 and 49.

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